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Position change of body in non-isolated system

  1. Nov 30, 2009 #1
    1. The problem statement, all variables and given/known data

    A body of mass 5 kg is initially at rest. At time t=0, a constantly increasing force is applied to the body for 7.5 seconds according to:F(t)=at; where a is a constant 0.866 N/s. Determine the distance x the body travels during the application of the force.

    2. Relevant equations
    delta E of system = sigma T
    sum of forces in y direction =0
    normal force - mass*gravitational acceleration=0
    work=force*change in position
    1/2mass*final velocity^2 = 1/2mass*initial velocity^2 + work

    3. The attempt at a solution

    At kind of a loss for where to start this problem because the force is not constant.
    Can I some how find a value for Work and use that to solve for final velocity and use that to find change in position? Please Help!
     
  2. jcsd
  3. Nov 30, 2009 #2

    ehild

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    Homework Helper
    Gold Member

    You can not use the work-energy theorem in this problem.
    Use Newton's Law: the acceleration is force/mass. Now the acceleration depends on time. Acceleration is the time derivative of velocity; you get velocity by integrating acceleration:

    [tex] v(t) = \int{a(t)dt}[/tex]

    the integration constant is detemined from the condition v(0)=0.
    Velocity is the time derivative of displacement: you get the displacement by integrating velocity: v(t)

    [tex] x(t=7.5) -x(0) = \int_0^{t=7.5}{v(t)dt}[/tex]



    ehild
     
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